MAST20026 - Real Analysis Notes

Description

This is a comprehensive compilation of information from MAST20026 lectures, the textbook, tutorials, practicals, workshops, problem booklets and other useful sources I found online to aid my study. Each section (particularly the harder concepts) is supported by easy to read and understand dot points, diagrams, pictures. Includes all summarised formulae required to know for each topic. Topics included are: 1. Logic and proofs (introduction to truth tables, first order logic, propositional logic, set theory, axioms for the real numbers, direct and indirect proofs, proof by contrapositive, proof by contradiction, proof by induction) 2. Sequences (epsilon proofs of sequences, limits, convergence/divergence) 3. Limits (rigorous limit proofs, convergence/divergence, continuity, intermediate value theorem, mean value theorem) 4. Riemann integration (introduction to integration, Riemann sums; upper and lower, definition of Riemann integrable) 5. Series (convergence, divergence, multiple tests including Divergence Test, Comparison Test, Ratio Test, Integral Test, Harmonic p-Series Test, Alternating Series Test, Absolute Convergence Test and Geometric Series Test, as well as introduction to power series and Taylor Series; radii of convergence, and an introduction to Fourier Series).